Page 20 of Katabasis
“Go on.”
He hummed as he flipped through her notes. “Where did you find all this?”
“The Dunhuang cave texts.”
“I couldn’t find any translations of the Dunhuang cave texts.”
“There aren’t any. You just don’t have any Asian languages.”
“Fair enough.” Peter read a while longer, tracing his finger over each page. It made Alice oddly nostalgic to see him bobbing his head as he went along, making sense of her furious scrawls. They used to do this in the lab—show each other their wildest ideas, and offer each other proof they weren’t insane. She had missed Peter’s mind. It was like wearing a parachute—she could trust that he’d catch any mistakes she’d made.
At last he said, “I think this checks out.”
“Thank you.”
“But that’s consistent with my map,” Peter continued. “That is—it’s just an oversimplified version of my map, if we take Hell as non-Euclidean.”
Alice had only been to one lecture about non-Euclidean geometries, and what she remembered was a lot of diagrams of potato chips and coral reefs. “I don’t know what you mean.”
“Suppose it’s less like a... what’d you say, a pizza anus? Less like that, and more of—well, a spiral.” He drew a diagram below hers to demonstrate.
“Suppose we’re in hyperbolic space,” he said. “Take the parallel postulate out of Euclidean geometry, and assume we are dealing with negative curvature. Then we might visualize the courts as a twisted pseudosphere, bounded on the outside, but infinite on the inside—”
“But we’re notinhyperbolic space,” said Alice. She did not know much about hyperbolic space, but this at least seemed obvious. “We’dknow, we’d see all sorts of—of freaky coral patterns around us, we wouldn’t be walking on this flat plane—”
“Actually no,” said Peter. “That’s the point. When you’re inside it, of course it’s going to look like a flat plane. We see the freaky coral because we’re three-dimensional beings visualizing two-dimensional hyperbolic space. But we’re not four-dimensional beings, so we can’t actuallyseethe wonkiness of three-dimensional hyperbolic space. Curved lines appear straight to us.”
“Oh, stop it.” As always, mathematics induced in Alice the acute urge to weep. “What’s thepoint?”
“The point is that we could just head to this peak here.” Peter tapped the top of the spiral. “The center of Hell, the point that oversees the rest of the Eight Courts.
“Sure,” said Alice. “Ifthat point exists.Ifthis is hyperbolic space. Which we don’t know.”
“I think we probably do, though,” said Peter. “I mean, how else to make sense of that weird view from above?”
“But that wasn’t a pseudosphere, that was just chthonic flux.”
“I don’t think so, Law. I interpret that as Hell signaling its geometry.”
Alice was unconvinced. “I interpret that as Hell screwing with us. It’s just as likely.”
They stared at the notebooks. This was an impasse. Two maps, and no good reason to prefer one over the other.
“I wish I could measure the speed of light here,” Peter said unhappily. “And also the size of the known chthonic universe.”
“Very helpful,” said Alice. It was clear to her now they would have to decide on pragmatics. If she let Peter go on, then he’d while away the day speculating about geometry. “I think we should go in order.”
Peter groaned. “But that’s such a waste of time.”
“So is hiking to a mythical peak whose existence is uncertain!”
“The peak is a shortcut. The peak keeps us from turning up every stone in the lower rocks—it lets us see everything at once, and then just—I don’t know, jump there—”
“Fine,” said Alice. “Say your peak exists. Where would you jump to? What sins do you think he’s committed?”
A silence. For once Peter had no easy rejoinder. They were both thinking, then, of undergraduates burned to a crisp, and whether that counted as murder, or just as lying. They were thinking of Olivia Kincaid and Elspeth Bayes and all the students who never graduated. They were thinking of everything Professor Grimes had done over his storied career and everything they didn’t know about. And Alice, for one, was thinking of cold laughter, fingers digging into her shoulder, hot breath on her face, a burning in her skin.
“Well,” Peter said lightly. “That’s just the question.”
